Spiral-wave dynamics in excitable medium with excitability modulated by rectangle wave

doi:10.1088/1674-1056/20/4/040503

Abstract We numerically study the dynamics of spiral waves in the excitable system with the excitability modulated by a rectangle wave. The tip trajectories and their variations with the modulation period T are explained by the corresponding spectrum analysis. For a large T, the external modulation leads to the occurrence of more frequency peaks and these frequencies change with the modulation period according to their specific rules, respectively. Some of the frequencies and a primary frequency f₁ determine the corresponding curvature periods, which are locked into rational multiplies of the modulation period. These frequency-locking behaviours and the limited life-span of the frequencies in their variations with the modulation period constitute many resonant entrainment bands in the T axis. In the main bands, which follow the relation T/T₁₂=m/n, the size variable R_x of the tip trajectory is a monotonic increasing function of T. The rest of the frequencies are linear combinations of the two ones. Due to the complex dynamics, many unique tip trajectories appear at some certain T. We find also that spiral waves are eliminated when T is chosen from the end of the main resonant bands. This offers a useful method of controling the spiral wave.

Keywords: spiral wave FitzHugh--Nagumo model frequency-locking

Received: 02 November 2010
Revised: 30 December 2010
Accepted manuscript online:

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	05.65.+b	(Self-organized systems)
	47.54.-r	(Pattern selection; pattern formation)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11005030), the Science Foundation of Hebei Education Department, China (Grant No. 2009135), the Science Foundation of Inner Mongolia Education Department, China (Grant No. NJ09178) and the Science Foundation of Hebei Normal University, China.

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Yuan Guo-Yong(袁国勇) Spiral-wave dynamics in excitable medium with excitability modulated by rectangle wave 2011 Chin. Phys. B 20 040503

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Spiral-wave dynamics in excitable medium with excitability modulated by rectangle wave

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